Cremona's table of elliptic curves

12240 = 2⁴ · 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	12240bm	Isogeny class
Conductor	12240	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	8846579462400000000 = 214 · 314 · 58 · 172	Discriminant
Eigenvalues	2- 3- 5+  0  4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1039683,-382120382]	[a1,a2,a3,a4,a6]
Generators	[352795:17305002:125]	Generators of the group modulo torsion
j	41623544884956481/2962701562500	j-invariant
L	4.4228697605358	L(r)(E,1)/r!
Ω	0.15018231385061	Real period
R	7.3625010281429	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1530c5 48960fd6 4080be5 61200ff6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240bm5

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	+	0	4	-2	+	-4	0	2	-8	6	6	4	0	10	-4	-2	-4	0	-6	-8	-12	6	-14

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Quadratic twists for elliptic curve 12240bm5

-4	8	-3	5
1530c5	48960fd6	4080be5	61200ff6

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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